Common Denominator for Value and Expectation No-go Theorems: Extended Abstract

TL;DR

This paper clarifies and compares two types of no-go theorems in quantum hidden-variable theories, focusing on projection measurements to unify their analysis and highlight their differences and similarities.

Contribution

It refines existing no-go theorems by focusing solely on projection measurements, enabling a clearer comparison of expectation and value no-go theorems in quantum theory.

Findings

Expectation no-go theorems do not subsume value no-go theorems.

Both approaches are valid and complementary when restricted to projection measurements.

Clarification helps in understanding the limitations of hidden-variable theories.

Abstract

Hidden-variable (HV) theories allege that a quantum state describes an ensemble of systems distinguished by the values of hidden variables. No-go theorems assert that HV theories cannot match the predictions of quantum theory. The present work started with repairing flaws in the literature on no-go theorems asserting that HV theories cannot predict the expectation values of measurements. That literature gives one an impression that expectation no-go theorems subsume the time-honored no-go theorems asserting that HV theories cannot predict the possible values of measurements. But the two approaches speak about different kinds of measurement. This hinders comparing them to each other. Only projection measurements are common to both. Here, we sharpen the results of both approaches so that only projection measurements are used. This allows us to clarify the similarities and differences between the two approaches. Neither one dominates the other.